Ed Goodwin, Principal of St Christopher's School, has also offered advice to parents and raised his concerns over cyber-bullying in a letter.
The school is having to tackle the new form of bullying and has been briefed on issues relating to internet safety by representatives from the TRA.
Mr Goodwin said: "It has become clear in countries around the world and in Bahrain, that respectable, well-brought up and generally well-behaved young people are amongst those writing Facebook comments about others that would horrify, embarrass and appal all reasonable parents. These obnoxious entries constitute bullying and harassment. In general, but not exclusively, this activity is happening at home - under the parent's noses.
"It has always been the case that in the adolescent years - and just before - children will do things that are the despair of their parents.
"Sometimes - and this is certainly the case with some of the social networking misuse we are seeing - this is the result of a peer pressure of a new type, one could perhaps call it 'cyberpeer pressure'. When friends - i.e. one's peer group - are seen to be ganging up on a person, it becomes difficult for some adolescents not to join in the harassment.
"It is the same kind of pressure that leads some to smoking, drugs and other undesirable behaviours. This does NOT however, excuse such behaviour.
"In our own school we have seen quite horrible comments about other youngsters that have been written by otherwise very well-behaved students who have supportive parents.
"In school, we are doing our best to ensure that access to such sites is controlled. Parents also need to take firm action at home to ensure that they know who their children are communicating with online - aside from bullying, there ARE adults out there who will hide on-line and who want to do harm to young people - don't make the mistake of saying "it could never happen to my family".
"As a school we have, of course always addressed these kinds of issues (peer pressure, bullying, being independent and so on) through a variety of means. We need now to check that we are keeping up-to-date in these matters and taking into account the impact of internet on young people. Our mantra - "learning, caring, communication" - demands no less."
Mr Goodwin has suggested that to protect children from cyberbullying - or from the temptation to engage in doubtful actions themselves, perhaps parents should insist that they have the means to access their children's social networking sites.
He advised: "Beyond all of these technical and reactive measures, it is more important that you talk to with your children about the issues and the need for them to be strong and independent in the face of peer pressure.
"Parents who are assiduous and successful in this will provide their children with an incredibly powerful life skill - one that will enable them as adults to stand up for what is right rather than to always take the easiest path. These will be the people who become leaders rather than followers.
"A final comment I would make is that these sites DO have value as well as danger - my belief is that we should educate children in the safe and proper use of social networking sites rather than simply ban, ban, ban!"